Let a1,a2,…,an,b1,b2,…,bn be positive reals such that a1+b1=a2+b2=…+an+bn and n√a1a2…anb1b2…bn≥n. Prove that n√a1a2…anb1b2…bn≥a1+a2+…+anb1+b2+…+bn.
Source: 2012 Indonesia Round 2 TST 2 Problem 3
Tags: inequalities unsolved, inequalities
Let a1,a2,…,an,b1,b2,…,bn be positive reals such that a1+b1=a2+b2=…+an+bn and n√a1a2…anb1b2…bn≥n. Prove that n√a1a2…anb1b2…bn≥a1+a2+…+anb1+b2+…+bn.